Problem: Simplify the following expression: $a = \dfrac{7}{z - 10} \div \dfrac{3}{3z}$
Solution: Dividing by an expression is the same as multiplying by its inverse. $a = \dfrac{7}{z - 10} \times \dfrac{3z}{3}$ When multiplying fractions, we multiply the numerators and the denominators. $a = \dfrac{ 7 \times 3z } { (z - 10) \times 3}$ $a = \dfrac{21z}{3z - 30}$ Simplify: $a = \dfrac{7z}{z - 10}$